If you want rare, try getting a pink tail in Final Fantasy IV. First, you have to go to the correct room in the last dungeon in the game. Then, there is a 1/64 chance that a random battle in that room will be against Pink Puffs, aka Flan Princesses. There is a 5/64 chance of getting an item after the battle (1/64 for each of 5 monsters), and a 1/64 chance that the item will be a pink tail.
Thus, your chances are 0.000019%, or 5 in 262144.
Consistently find pink tails faster than you discover resources from mines in Civ IV, and we can talk about it being broken.
I have personally experienced the resource-finding phenomenom once; I have yet to find a pink tail.